This invention relates generally to sonar systems, and more particularly to analog signal processing within high resolution systems so as to form directional beams. A continuous analog sampled data technique of beamforming has been used in sonar applications wherein the narrowband signal from each hydrophone is divided into its sine and cosine (quadrature) components, (X.sub.i [t] and Y.sub.i [t]). Once represented in this form, the phase shift operation required to cancel the equivalent time delay associated with the element's relative position can be achieved by the common vector rotation equations: EQU X.sub.n =cos .theta..sub.i X.sub.i +sin .theta..sub.i Y.sub.i EQU Y.sub.n =-cos .theta..sub.i Y.sub.i -sin .theta..sub.i X.sub.i
where:
(X.sub.i, Y.sub.i) is the original quadrature pair, PA1 .theta..sub.i is the desired angle of rotation, and PA1 (X.sub.n, Y.sub.n) is the phase shifted quadrature pair. PA1 Y.sub.i is the second sample from element i, taken 1/4 cycle later, PA1 n is the number of elements used to form a beam, PA1 X.sub.m is the real part of the m.sup.th beam formed, PA1 Y.sub.m is the quadrature part of the m.sup.th beam formed, and PA1 Z.sub.m is the beam magnitude of the m.sup.th beam.
To form a directional beam, the quadrature signals from each element are phase shifted such that planar acoustic signals arriving from the desired angular direction add coherently after phase shifting. To obtain the desired beamwidth and side lobe suppression, the phase shifted quadrature signals are amplitude shaded by a factor, W.sub.i, according to their relative position in the array. The resulting signals from n elements are then linearly summed to form two equations: ##EQU1## The magnitude of the resulting beam is: ##EQU2## A physical implementation of this method comprises a set of weighting and summing transformers. The signal from each array element is divided into its sine and cosine components to produce the X.sub.i and Y.sub.i outputs.
The weighting of each output is accomplished by scaling the number of turns on the weighting and summing transformers. The sign of the required weighting coefficient determines the sense of the winding. Since each transformer has two windings from each element, the output of the transformer is the sum of the weighted and shaded inputs to the transformer. One transformer performs the X summation as in Eq. (1), and the other performs the Y summation. Only one beam is formed with each set of hardware. U.S. Pat. No. 3,274,536 to F. R. Abbott et al is representative of such a system.
The beam may be steered by mechanically rotating the array to point in the desired direction. Alternately, the number of elements in the array can be increased, and, in the limit, elements can be spaced at intervals around the face of a cylinder for 360.degree. coverage. By selecting the appropriate group of elements, the beam can be steered through 360.degree.. This procedure results in the desirable effect of eliminating the delay associated with mechanical slewing.
In most applications, it is advantageous to form more than one beam during a pulse length, so that the sonar can "look" in more than one angular direction at a given range increment and still satisfy the Nyquist criterion. As the pulse length is shortened, the time available to multiplex between sets of elements decreases, so that it is impractical to have one continuous analog beamformer form many beams. In the limit, a beamformer is provided for each direction in which a beam is to be formed. If R components are required to form one beam and N beams are needed to cover a given area, R.times.N components are needed for the sonar. In addition, the output of each beamformer is usually multiplexed for a serial presentation of the N beam magnitudes. The implications for sonars with close element spacing and with large numbers of elements per beam are shown by the following example.
A sonar covering 120.degree. is designed with a 150 .mu.sec pulse length and the elements are spaced at 3.degree. on the face of a cylinder. For each range increment, it is desired to inspect the output of 40 beamformers so that the entire 120.degree. can be viewed. Assume that for the desired beamwidth and sidelobe suppression, 15 elements are used to form a beam. For one beamformer, two transformers are needed, each with 30 (2 times 15) windings on the primary. If 40 beamformers are needed, 1200 windings on 80 transformers will be required and over 2400 connections will be needed to make the transformers operational. In addition, 40 magnitude circuits are needed to convert the X and Y outputs to a single quantity. After the magnitude is calculated, the outputs are multiplexed to a single line for a serial output. The large number of components and the larger number of interconnections between components needed by this beamforming technique is a disadvantage when space and cost are considered.
A more efficient organization allows multiple beams to be formed in one beamformer in a time-serial fashion. One such architecture, U.S. Pat. No. 3,370,267 to H. J. Barry, sequentially sampled elements to 1-bit accuracy and shifted the samples through a shift register. The output of each stage had an appropriately chosen weighting resistor attached between it and a summing amplifier. The summing amplifier added all the weighted outputs together. In this manner, successive beams were formed by shifting the sampled data through the shift register. The formed beam had no phase shift correction for the cylindrical array used, and was limited in dynamic range by the coarse signal amplitude quantization.
Digital beamformers have also been proposed which use quadrature sampled data that is quantized in nonlinear steps. By using geometric encoding of data, multiplication operations become additions of geometric data. Both phase shifting and amplitude weighting are accomplished before the geometrically encoded data is converted to its linear representation for summation in a linear accumulator. Multiple beams were formed serially in one beamformer, with element samples serially shifted past one phase shifting and amplitude shading operator.
The basic algorithm used is based on taking two element samples spaced 90.degree. apart in time at each element once each scan. The sampled values from estimates of the continuous quadrature components of the narrowband element signals. Provided that each element is sampled at least twice in 1/W seconds, where W is the signal bandwidth, the samples hold sufficient information for a valid phase shift and summation process similar to the continuous analog technique discussed earlier. The beamforming equations for the sampled case are: ##EQU3## where X.sub.i is the first sample from element 1,
For a cylindrical array, the set of element phase shift values for each beam is identical to the set for the next beam, so that one set of values is used for all beams formed. If the quadrature sampled element values are applied in serial order to the phase shifting device, beams will be produced with each added element pair (X.sub.i, Y.sub.i). This is directly analogous to the cross correlation process. Disadvantages of this method include the need for analog to digital conversions, the added error introduced by geometric quantization, and the relative slowness of the beam formation because of the serial element shading technique of the processor.